Pushpin mount can be OK if you do it properly.
It is a pain, but the ONLY way to mount the cooler is to do it with the motherboard outside of the case.
1) The pushpins are hard to get down. If you try to do it with the mobo in the case, you will bend the motherboard and possibly cause other problems. Just put the mobo on a piece of cardboard.
2) You need to be able to look at the back of the motherboard to be certain that all 4 pins are through and locked.
First, look at the cooler, and play with the pins, until you understand how they work. Read the Intel instructions that came with your cpu. The trick is to push in a diagonal pair of pins at the same time.
I agree with BeCoolBro that backplate mounts are better, particularly if the cooler is large and heavy.